All state-owned property is off limits -big fines possible. Some counties don't allow it either: Hennepin, Dakota, Scott, maybe others. I think Ramsey County parks wants you to get a permit but think they are free?
It's best not to ask permission in city parks or public schoolyards, but best to detect schoolyards when school isn't having classes. Just don't do damage & the worst they can do is ask you to leave & that's unlikely.
The reason it's best not to ask is because desk-bound bureaucrats will just quote you laws about property damage that existed long before metal detectors were invented. Yes, those old laws say no disturbing the soil, no removing anything, that's what they'll quote you but on city park or public school property it would be unlikely they'd do anything as long as you aren't doing damage. HH, George (MN)